Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}5x+y &= 7 \\ 4x-y &= 8\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = -4x+8$ Divide both sides by $-1$ to isolate $y$ $y = {4x - 8}$ Substitute this expression for $y$ in the first equation. $5x+({4x - 8}) = 7$ $5x + 4x - 8 = 7$ Simplify by combining terms, then solve for $x$ $9x - 8 = 7$ $9x = 15$ $x = \dfrac{5}{3}$ Substitute $\dfrac{5}{3}$ for $x$ back into the top equation. $5( \dfrac{5}{3})+y = 7$ $\dfrac{25}{3}+y = 7$ $y = -\dfrac{4}{3}$ $y = -\dfrac{4}{3}$ The solution is $\enspace x = \dfrac{5}{3}, \enspace y = -\dfrac{4}{3}$.